In this article, John McCauley uses his experience as an Architect and Construction Manager to critically analyse the construction scheme for building the Khufu pyramid and the popular theory of the use of an internal ramp.
There has been an innumerable quantity of books written about the construction of the pyramids at Giza, Egypt. So too have there been any number of different theories on how the construction of these pyramids was accomplished, with each new or expanded theory accompanied by a description stating that it was the “definitive” solution, or “the puzzle finally solved”, etc. Of late, a few authors have focused on the “internal ramp solution” as being the most plausible explanation on how the ancient Egyptians built the Great Pyramid. Indeed, some Archaeologists have also acclaimed this “internal ramp solution” as a creative explanation for this ages-old construction mystery. Most Archaeologists, however, lack the technical training or understanding of the nature of structural forces to make a qualified endorsement of this proposed solution. Let me first state that this “internal ramp solution” represents a complete lack of understanding on how gravity affects structures and why this theory bears no serious thought in the academic world. Before I get into an analysis of why “internal ramps” do not work, let me state very clearly that I honestly do not know exactly how the Great Pyramid was actually built, but I think there are clues that may lead to a reasonable explanation in the future.
Let me first outline some of the facts that we do know about the Great Pyramid of Giza:
This pyramid appears to be the final evolution of pyramid building that evolved from the mud brick mastabas which were supposedly the resting place of important dignitaries.
The Great Pyramid has only one cartouche above the King’s chamber that purports to indicate that it is the burial chamber of Khufu (Cheops).
This pyramid was covered with smooth white casing stones that partially collapsed after a severe earthquake and were later used as a “quarry” to construct some buildings in Cairo, notably the Mosque and Madrassa of Sultan Hassan (completed in 1359). Some of these stones contained hieroglyphics. The Greek historian Herodotus claims to have seen the Great Pyramid before the casing stones were removed.
If some of the casing stones did contain hieroglyphics and if these stones were scattered around Lower Egypt, finding them and deciphering them could lead to some further understanding as to the construction of the pyramid.
As a retired Architect and Construction Manager with a strong background and interest in Archaeology, I am focused on how ancient cultures built their megalithic monuments. Since many of the very old cultures left no “construction manual” on how they built their monuments, we are forced to reverse engineer the remains of what we observe of their work. We can apply our knowledge of the ancient’s religion, tools and tool marks, hieroglyphics, myth, etc. and weigh these attributes against what we observe but ultimately it is only our best educated guess on how and why certain construction techniques were used. We can also discount certain theories, such as the application of “anti-gravity”, and the like, as being without validity or in the realm of unproven wishful thinking. In the end, we have to make a judgment that makes the most common sense given what we know about the culture and their construction expertise.
So, let me outline some of the thought process that comes to mind when analyzing this “internal ramp approach”. There are some inherent difficulties in building an internal ramp and moving stones on it, as follows:
CONSTRUCTING THE INTERNAL RAMP WOULD BE VERY DIFFICULT:
The ancient Egyptians employed two methods for spanning an opening: large granitic stones from the quarries at Aswan were placed above the opening which divert the structural forces around the opening, such as at the “King’s Chamber”, or corbelling stone over a void as we see in the “Grand Gallery”.
The "King’s Chamber" is a good example of the difficulty in constructing a void in such a structure. The King’s Chamber required granite stones which weigh about 60-tons each. Stone is not good in bending – only in compression – so the size and depth of these granite stones must be large enough to transfer the loads from above to the stone walls on either side of the void. These granite slabs have a tendency to collapse downward, and their bases spread outward from the loads above, but these movements have to be resisted by the tremendous weight of core blocks against the slabs, especially at the base of the slabs.
The "Grand Gallery" is another example of a void in the Great Pyramid. This Gallery solution was solved by slightly "corbelling" the stones over each other; that is, a slight overhang of each successive course over the course below. To create even a minimum 6-foot wide “internal ramp”, there would have to be quite a few corbelled tiers of stones, thereby creating a void that would be quite considerable in volume. If, for instance, each course was cantilevered 6” above the course below, it would take six courses of stone to cantilever three-feet; half the width of the void. The height of these six courses would be about 18’-21’ high, on top of two vertical courses, thereby creating a void 6’-0” wide at the base and 27-feet or higher. This void would have to occur around the entire pyramid, all the way to the top. As the pyramid grew taller, the amount of void space would eventually be greater than the amount of remaining stone!
The complexity of creating such an internal ramp, using corbelled stones or granite slabs, is further compounded by the following realities:
Such a void would have to be quite a bit inboard of the outer face of the pyramid so that there is enough solid pyramid stone above the void thereby allowing an adequate pathway for the structural transfer of loads to the walls of the void. Even so, as the ancient Mayans intuitively understood, there would be a tendency to "spread" the ceiling stones of the internal ramp apart, leading to instability and collapse; the Mayans solved this by installing timber tie-beams across the spring point of their vaulted ceilings.
Following this train of thought, there is a reason why the King’s Chamber is approximately in the center of the pyramid; the tendency of the granite roof slabs to "spread" is limited by the equal dead weight of the pyramid mass on either side of the spring point of these stones. If the Chamber was closer to the outboard face of the pyramid, there would be an unequal dead load resisting the spread of the granite slabs and the “outboard” limestone core blocks could not resist the horizontal thrust forces.
If the internal ramp could be constructed without “corbelling”, it would require a significant amount of very stout granite slabs, and the question is, how would these much larger and heavier stones be placed? Using the King’s Chamber as an example, each one of these void ceiling stones in the internal ramp could weigh 20-30 tons, or more, each. That is an enormous amount of Aswan granite to haul up the pyramid ramps just to form the internal ramp as it advances!
For an internal ramp to make any sense for building the upper two-thirds of the pyramid – assuming that the bottom third was constructed with an external ramp – the entire length of the internal ramp would have to be maintained for the entire duration of the construction phase. This would create quite a large "hollow" space around much of the perimeter of the entire pyramid. This would be a considerably unstable exterior for the entire pyramid. And, given the frequency of earthquakes in the area, the probability of a catastrophic failure of the pyramid would be assured. Since we know that a catastrophic earthquake dislodged the casing stones, it would have also have impacted such an unstable internal ramp.
Even if the internal ramp was used, and it had to be somewhat "inboard" of the perimeter of the pyramid, it begs the question, once a stone is delivered to the head of the internal ramp, how is it placed between the side of the internal ramp and the exterior plane? Even more difficult would be the placement of the final casing stones if the internal ramp already existed. This leads to a further question and that is; in the internal ramp scheme, how are the casing stones placed and how are they dressed and carved with hieroglyphics?
One would also question what becomes of the sleds that were dragged up the ramps once they delivered their cargo of limestone core blocks.
The ancient Egyptians had no ability to empirically determine the size and spanning ability of stone. Their entire building technology was developed over millennia by the "trial and error" method. The failure of the earlier "bent pyramid" attests to that. So, there doesn’t appear to be any precedent for having built such an internal ramp either before or after the Khufu pyramid. It is therefore seemingly illogical to conclude that such a challenging and unique "solution" would have been devised "out of the blue" and used just once.
Egyptologists have demonstrated the feasibility of a number of ancient Egyptian technologies and construction techniques through actual example in the field. This approach is admired to solving a problem. However, the use of highly sophisticated 3-D computer technology software programs that were used to graphically show an internal ramp, only demonstrates that something can be drawn, but does not support the probability that it can actually be built in the real world. Yes, some complex shapes can be drawn and built, but just because a complex shape can be drawn does not mean that the shape makes any sense to actually build. Computer graphics can mislead us into believing that since something is in the memory cells of our hard drive, it must be buildable and therefore the solution must be correct!
The slope of a six-foot wide ramp would require a great amount of work to maintain. As this ramp sloped higher and higher, the corbelled vault above it would have to be elevated also. This would introduce a level of complex geometry that would slow construction and add unnecessary difficulty.
To pull a 2.5-ton stone efficiently, the surface on which it is pulled needs to have a low coefficient-of-friction. This is difficult to attain between a sled and stone and the sloped ramp surface, and at the same time provide a reasonable surface on which the “pullers” are able to gain traction.
As a ramp ascends upward at, say 6-degrees, it would rise approximately 24" every 21′ of run. If the run was 100′, the rise would be about 10-feet’. To make a complete four-sided turn around the pyramid, the rise in this internal ramp would be over 40-feet. This would require that virtually every course be sloped to allow for a continuous 6′ wide x 6′ high passage, plus the height of the corbel vault. It would also require that every corbelled course change in elevation to allow for headroom. This would require an unwarranted amount of labor and skill to create such a ramp.
THE 90-DEGREE CORNER CONUNDRUM:
As we all know from the evaluation of the many proposals and theories on "spiraling ramps" on the outside of a pyramid, the right angle corners are critical to maintaining the correct geometry of the four sloping sides. Otherwise, the four sloping planes of the sides and their intersecting corners will not meet at a common apex point. The “internal ramp” scheme proposes that the corners were used to possibly mount a "crane" of sorts to transfer the limestone blocks from one internal ramp slope to the next portion of the ramp. In this approach, this open corner is required since the crew who are pulling a 2.5-ton stone could not make a right-hand or left-hand turn to begin ascending to the next ramp. One can also look at the physics and dimensional requirements of moving such a stone up a 6′ wide ramp and come to the following conclusion:
A 2.5-ton stone in a 6′ wide ramp leaves no room for more than one rope to pull the stone and a maximum of one puller on each side of this rope, forming a column of multiple pullers.
A 2.5-ton stone = 5000# ; each "puller" can exert approximately 100# –125# of pulling force, at best, on a level plane. This would result in 20-25 "pullers" when the coefficient-of-friction of a sled and stone was 0.4–0.5. However at a 6-degree slope (the near maximum attainable slope for “pulling” in ancient Egypt), the number of pullers would have to increase to perhaps 30-40 pullers. If these pullers were spaced 5′ apart and the puller nearest to the stone was at 8′ from the stone, the total pulling column would be 20 pullers x 5-feet, plus 8-feet, plus the length of the sled, or about 115-feet long. Assuming that the first puller in the column didn’t want to fall off the pyramid, the rear of the stone would be about 115-feet from the edge of the pyramid at the head of the ramp so that a crane could lift it and then rotate it to the next upward sloping ramp. This required space would result in a large corner opening of 115-feet x 115-feet on each side; an enormous opening that would be very difficult to fill in later because of its location.
If each corner had such a large gap, one would certainly question not only the feasibility of closing in such an opening later in construction, but in maintaining the geometry of the four sloped sides and the diagonal lines of the corners.
By even a conservative calculation, core stones for the pyramid had to be delivered every minute and returning timber sleds had to be recycled down the same internal ramp. This would not be possible within such a confined space as an internal ramp.
The internal ramp is too dimensionally restrictive and requires a high level of specialized stonemasonry when construction duration may have been a strong or real consideration.
In reviewing other rational approaches to building a pyramid, a combination of outside earthen ramps and exterior “ledge ramps” should be considered. The external ramp approach should not be discounted so quickly by those who are infatuated by the new and novel “internal ramp solution”. A continuous ledge ramp corkscrewing around the outer edge of the pyramid is a real possibility.
There is a guiding principle in building construction throughout the ages and that is, "keep it simple"! The derivation of the smooth-faced pyramid seems to have logically evolved from stacking mastabas on top of each other – much like a wedding cake – and then filling in the ledges. It would seem that these ledges could also serve as opportunities to transport stone blocks from one level to another without the need for an internal ramp. Why make it unnecessarily complicated?
We may never figure out exactly how the Khufu pyramid was built but deductive reasoning would certainly eliminate certain theories due to their complexity, cost and structural limitations. Undoubtedly, a combination of short external ramps, ledge ramps, and leveraging "machines" were used because they were effective and simple solutions that abounded in ancient times.
The process of building a pyramid was definitely evolutionary with some very innovative techniques developing with each new pyramid. The knowledge had to be cumulative and was passed on through guilds of expert craftspeople and builders! Each disaster and each success gave the Egyptian architects a better intuitive understanding on how the forces of gravity worked and how those forces could be overcome by an altered design and construction approach on the next pyramid. Let us remember, the ancient Egyptians did not have the empirical knowledge we now have about structures; they either had an intuitive sense of what would work, or it might fail. Knowledge was built on the try-and-fail method.
The main argument against the exterior corkscrewing ramp seems to be that it might obscure the sightlines on the four corners of the pyramid such that the apex of the pyramid could not be observed as it is being constructed. However, if one uses a simple sighting board, it is easy to see how the slope of all of the edges of the pyramid can easily be maintained to converge at the same top point in space. The use of "offset" stakes was probably also a technique that the Egyptians used to confirm slopes and measurements from level to level. The Egyptians had figured this out centuries previously; geometry could be maintained from the uninterrupted side angles as well as the corners. This argument about the angle of the pyramid not being maintained because of some obscure problem at the corners doesn’t seem to make a lot of sense.
The French team that recorded "anomalies" cork-screwing around the perimeter of the pyramid appear to have jumped to the conclusion that the images represented evidence of this internal ramp. However, that may not have been the proper interpretation. If, for instance, the pyramid was constructed with an external ledge ramp along the perimeter and then the ramp was filled in with finished stones as the pyramid was being finished from the top down, these final stones would have been taken from a different location in the quarries than the original core stones. The different locations where stones were quarried would have slightly different densities, aging properties and moisture retention. Micro gravimetric readings of the entire pyramid would probably show similar corkscrewing anomalies just because the perimeter stones which filled in the abandoned ramp came from a different location in the quarry and have a different density.